Hypergeometric representation of a four-loop vacuum bubble

Abstract

In this article, we present a new analytic result for a certain single-mass-scale four-loop vacuum (bubble) integral. We also discuss its systematic $\e$-expansion in $d=4-2\e$ as well as $d=3-2\e$ dimensions, the coefficients of which are expressible in terms of harmonic sums at infinity.

5 pages, to appear in the proceedings of the conference "Loops and Legs", Eisenach, 2006

References in corpus (15)

• Harmonic Polylogarithms
• Harmonic sums, Mellin transforms and Integrals
• The pressure of hot QCD up to g^6 ln(1/g)
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• QCD Decoupling at Four Loops
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Explicit solutions of the multi-loop integral recurrence relations and its application
• Explicit solutions of the 3--loop vacuum integral recurrence relations
• - XSummer - Transcendental Functions and Symbolic Summation in Form
• Expansion around half-integer values, binomial sums and inverse binomial sums
• Four-Loop Singlet Contribution to the $\rho$ Parameter
• High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles
• Automatic reduction of four-loop bubbles
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• Tuning FORM with large calculations

Cited by in corpus (16)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Heavy Quark Masses from Sum Rules in Four-Loop Approximation
• Low energy moments of heavy quark current correlators at four loops
• The second physical moment of the heavy quark vector correlator at O(alpha_s^3)
• Anomalous magnetic moment with heavy virtual leptons
• All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
• Four-loop Standard Model effective potential at leading order in QCD
• The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops
• Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
• Application of the DRA method to the calculation of the four-loop QED-type tadpoles
• Standard and epsilon-finite Master Integrals for the rho-Parameter
• Life of Π
• New Results in Four and Five Loop QED calculations
• Hypergeometric functions with rational arguments
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals